col3.z

#############################################################################
##
#W  col3.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1110 ] :=
[ 8621401744799, 8686732088735, 9569553386878367, 7954662815, 30152467871,
2633640447, 33505114338719, 913716253, 33441477050231, 2868058579287,
37190746611727775, 1439 ]; 

PROPERTIES_SMALL_GROUPS[ 1110 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1116 ] :=
[ 2227889839780872927059, 1997230365461727059, 555853781640776283031,
14393602639368927059, 665756100082945878301771, 13884825721500959,
1996317130273200959, 600023075294401201771, 1789699374000959,
1488010587117093900, 2259624565177282737029, 12897463431600959,
498076866914426131, 596555201225329201771, 12342164400959,
11913414892094727929, 11914328203512327059, 13295371025365483527059,
1789624651527929, 12897463358727929, 445511947553101, 14393602640875527059,
497191422956283031, 16063260653067201900959, 111078629100959,
11914302811737600959, 30784326148570437029, 1788906124800959,
1789700832000959, 1996317131731200959, 619227556200993567483031,
21422744055921319260533100959, 13785308352000959, 15412834455206400959,
445535251226131, 15384423807331200959, 17200723264760649600959, 1692057600959
, 1333346055263100, 2024753155805637029, 11548915200959, 401241601771,
12897464889600959, 445513478426131, 14393602641628800959, 959 ]; 

PROPERTIES_SMALL_GROUPS[ 1116 ] := rec(
isNilpotent := [ 6, 15, 25, 46 ], 
isSupersolvable := [ 1, -9, 12, -26, 28, -30, 33, -38, 41, -46 ], 
isAbelian := [ 6, 15, 25, 46 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 27, -28, 34, -41, 44,
-46 ], [ 7, -16, 19, -20, 23, -26, 29, -33, 42, -43 ], [ 1, -6, 17, -18, 21,
-22 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 21, 25, 30, 34, 38, 42, 46, 50
, 54, 58, 62, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67 ], pos := [ 1, 2, 3, 4,
5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
] ) );

SMALL_GROUP_LIB[ 1122 ] :=
[ 505414047, 304087545, 569858064799, 35654129, 565294663967, 339204902681,
639383497081247, 415 ]; 

PROPERTIES_SMALL_GROUPS[ 1122 ] := rec(
isNilpotent := [ 8 ], 
isAbelian := [ 8 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -8 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1125 ] :=
[ 21330133005695, 18958266751, 24419867035796863, 20971525503, 20973618559,
21254637622655, 23328972702079, 16781695, 18874751, 18893246847,
106395232044511, 2097153407, 94573363583, 383 ]; 

PROPERTIES_SMALL_GROUPS[ 1125 ] := rec(
isNilpotent := [ 1, -2, 4, -6, 8, -10, 12, 14 ], 
isSupersolvable := [ 1, -2, 4, -6, 8, -10, 12, 14 ], 
isAbelian := [ 1, -2, 4, 8, 12, 14 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 14 ], [ 7, -10, 12,
-13 ], [ 2, -6, 11 ], [ 1 ] ] ),
frattFacs := rec( frattFacs := [ 7, 14, 15, 21, 34, 40, 41, 47 ], pos := [ 1,
2, 3, 6, 7, 10, 11, 12 ] ) );

SMALL_GROUP_LIB[ 1128 ] :=
[ 4305096071833714745, 193393762005689738949, 218148343365521049347323,
537658671166143739, 201973620842279644699, 201973620842073681723,
227826244636874562432251, 201973620845163126363, 227826244636877651876891,
227826244636877445913915, 256988003950721060515961595,
5492247888178336173567592, 218147984767796086547217, 171448116115207729,
193393603406989419569, 171448115909244753, 171448118998689393,
4856136928978671308437, 3816583333306805, 4305085951014752181,
3816583127343829, 3816586216788469, 246071330780031225357095675,
193393920619631126043, 218148342889720005563419, 193393920619425163067,
193393920622514607707, 475804339191611, 475807428636251,
605942749124196051707, 9699373850772915581468, 10940894372789092638241324,
404140569935119486053, 179054338293182555, 11422990054207532, 151878746206299
, 3400860661783, 171448128884910171, 91 ]; 

PROPERTIES_SMALL_GROUPS[ 1128 ] := rec(
isNilpotent := [ 4, 28, -30, 39 ], 
isSupersolvable := [ 1, -11, 13, -30, 34, 36, -39 ], 
isAbelian := [ 4, 28, 39 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 34, 36, -39 ], [ 5, -33,
35 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32 ],
pos := [ 1, 2, 3, 4, 11, 12, 17, 22, 27, 30 ] ) );

SMALL_GROUP_LIB[ 1140 ] :=
[ 402939602380521413, 404353671023735855, 459352488303584166959,
353519127850949, 600567718051781, 106033729999215, 685990992239969327,
35386017431293, 684648685700968859, 120878639051321469, 782029739561465107115
, 8823226291883,
[ (1,2,3,4,5), ( 3, 4, 5)( 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,
     22,23,24) ],
2614802047208417375279, 2980874250663718846350383, 404351263137780107,
353463255208331, 354701481560459, 402940784734230923, 120737173232390511,
2615083684529633608751, 137640360033068265597, 2981195400367779569308331,
2012222670557579, 671092561466351, 2296685839810425227, 106035542089113,
2293935408150967691, 3822822555662481803, 2618221857220262836619,
317326492043, 105910014430188, 404351316529535609, 526539461003, 93117911673,
601744267008395, 31200548095, 600567837088751, 106033849036185,
685990992298540427, 395 ]; 

PROPERTIES_SMALL_GROUPS[ 1140 ] := rec(
isNilpotent := [ 12, 41 ], 
isSupersolvable := [ 1, -12, 14, -31, 34, -41 ], 
isSolvable := [ 1, -12, 14, -41 ], 
isAbelian := [ 12, 41 ], 
lgLength := rec( lgLength := [ 4, 5, false ], pos := [ [ 16, -19, 24, -41 ],
[ 1, -12, 14, -15, 20, -23 ], [ 13 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 ]
, pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ] ) );

SMALL_GROUP_LIB[ 1144 ] :=
[ 48071235098723913, 58751655297497291, 67767336421952873591, 668108235433079
, 67179819870312806603, 76854269373233738572919, 624309834019608695,
624309834019359863, 714210450518829524087, 624309834023092343,
714210450518833256567, 714210450518833007735, 817056755393941092050039,
67211833044380821787, 51356281707803, 58751602301492507, 51356281458971,
51356285191451, 54993441656690059833, 42020264320569, 48071190256442937,
42020264071737, 42020267804217, 77525832200299370062967, 59237181216036983,
67767335838965127287, 59237181215788151, 59237181219520631, 582991727735,
582995460215, 763649461225792631, 67766701545362672759, 58723620744712475,
67180305396231097463, 545725028892791, 44877348983, 36723622029,
51780290936951, 119 ]; 

PROPERTIES_SMALL_GROUPS[ 1144 ] := rec(
isNilpotent := [ 4, 29, -31, 39 ], 
isAbelian := [ 4, 29, 39 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 35, -39 ], [ 7, -34 ], [
1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35 ],
pos := [ 1, 2, 3, 4, 5, 6, 13, 18, 23, 28, 31 ] ) );

SMALL_GROUP_LIB[ 1148 ] :=
[ 7532792382405, 58737379848039, 67677563251200239, 376179200239,
67415422487048039, 77393151314291200239, 308516208640239, 51200000239,
6635521565, 58952376320239, 239 ]; 

PROPERTIES_SMALL_GROUPS[ 1148 ] := rec(
isNilpotent := [ 4, 11 ], 
isAbelian := [ 4, 11 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -11 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1150 ] :=
[ 478479069013817, 2899295153699, 563939772019693853, 2759068707, 2526218243,
367315325, 2904815630595, 415600139001, 3340566434582915, 1539 ]; 

PROPERTIES_SMALL_GROUPS[ 1150 ] := rec(
isNilpotent := [ 4, 10 ], 
isAbelian := [ 4, 10 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, 8, -10 ], [ 1, -4, 6, -7
] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1155 ] :=
[ 47479201359, 21761359, 5441395, 1359 ]; 

PROPERTIES_SMALL_GROUPS[ 1155 ] := rec(
isNilpotent := [ 4 ], 
isAbelian := [ 4 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1156 ] :=
[ 789677208203755775, 48486482175, 1054675435115312527507711, 682530436284671
, 33816831, 582406442767, 682500807524607, 9697296639, 673065988067087,
912037982076450963711, 912037976141745684735, 13218614378719412479,
9891685073151, 505413887, 590393377023, 255 ]; 

PROPERTIES_SMALL_GROUPS[ 1156 ] := rec(
isNilpotent := [ 2, 5, 8, 16 ], 
isAbelian := [ 2, 5, 8, 16 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 13, 15, -16 ], [ 4, -5,
7, -8, 10, -12, 14 ], [ 1, -3, 6, 9 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 22, 15, 19, 23 ], pos := [ 1,
2, 3, 4, 5, 6, 7, 8 ] ) );

SMALL_GROUP_LIB[ 1160 ] :=
[ 1139913620196955971, 10253980090403655003, 11916652097544106071151,
47509912084010095, 11887777780941913591131, 1320780463751908824899,
16034987996631836845294015599, 16034987985628508509533426799,
44430130471239226264441967, 13789844261003540601295983, 33018857351300724847,
33018857351283514479, 38301874555589328753775, 33018857351541669999,
38301874555589586909295, 38301874555589569698927, 44430174484511682153649263,
11894607424764867485003, 8839626145612107, 10253971913361916235,
8839626128401739, 8839626386557259, 1322298162731887093427, 982683959921331,
1139912210546772659, 982683942710963, 982684200866483,
13823316385760020637324399, 10272975879000963183, 11916652056658037176431,
10272975878983752815, 10272975879241908335, 40886344260719, 40886602416239,
55064110704835269743, 16035021428879013841504279663, 38302594809161875404911,
11916608226593350655087, 10248084422961440075, 1138603988775923379,
13823265504852201050971247, 13823265514337828926626927,
38301836613105328299119, 11887796776730493688943, 28464507957674095,
7615518998639, 848126935799, 8855981743472751, 111 ]; 

PROPERTIES_SMALL_GROUPS[ 1160 ] := rec(
isNilpotent := [ 4, 33, -35, 49 ], 
isAbelian := [ 4, 33, 49 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 45, -49 ], [ 11, -44 ],
[ 1, -10 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35, 38
, 41, 44, 47 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 17, 22, 27, 32, 35
] ) );

SMALL_GROUP_LIB[ 1164 ] :=
[ 3539997634650448991, 3041329375355999, 50751600417793, 4812963018974303,
5602298350311309503, 12654669201599, 6518881581679833523295, 3041255906869439
, 5598442940689032287, 6516587567059961905343, 4914118070894783,
1500285763775, 151902576368640, 2013103924496400479, 4133939577023,
46204461985, 4812964292985023, 191 ]; 

PROPERTIES_SMALL_GROUPS[ 1164 ] := rec(
isNilpotent := [ 6, 18 ], 
isSupersolvable := [ 1, -12, 15, -18 ], 
isAbelian := [ 6, 18 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 8, 11, -18 ], [ 1, -7, 9,
-10 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );